All categories

3 years ago

I need help on number 10

Mathematics

1 answer:

adelina 88 [10]3 years ago

8 0

$180 - 41 = 139$

since <suq Must equal 180 So 180 minus <sur equals <QUR

You might be interested in

Precal help if you could could you answer both. Me finishing this helps me graduate.

oee [108]

Exercise 1:

The easiest way to compute powers of complex numbers is to write them in the form

$z = \rho e^{i\theta} = \rho(\cos(\theta)+i\sin(\theta))$

In this form, you have

$z^n = \rho^n e^{in\theta} = \rho^n(\cos(n\theta)+i\sin(n\theta))$

The magnitude of the number is given by

$z=a+bi \implies \rho = \sqrt{a^2+b^2}$

So, we have

$z=-1+\sqrt{3}i \implies \rho = \sqrt{1+3}=2$

As for the angle, we have

$z=a+bi \implies \theta = \text{atan2}\dfrac{b}{a}$

So, we have

$z=-1+\sqrt{3}i \implies \theta = \text{atan2}\left(\dfrac{-\sqrt{3}}{-1}\right) = -\dfrac{2\pi}{3}$

Finally,

$z=-1-\sqrt{3}i = 2\left(\cos\left( -\dfrac{2\pi}{3}\right) + i\sin\left( -\dfrac{2\pi}{3}\right)\right) \implies z^6 = 2^6\left(\cos\left( -4\pi\right) + i\sin\left(-4\pi\right)\right) = 64$

Exercise 2:

You simply have to compute the trigonometric function:

$\cos\left(-\dfrac{\pi}{4}\right) = \dfrac{\sqrt{2}}{2},\quad \sin\left(-\dfrac{\pi}{4}\right) = -\dfrac{\sqrt{2}}{2}$

So, we have

$z = \sqrt{2}\left(\dfrac{\sqrt{2}}{2} - i\dfrac{\sqrt{2}}{2}\right) = 1-i$

7 0

3 years ago

Topic: Solving exponential equations. Solve for the value of x. 1. 5^x+1= 5^2x-3

liraira [26]

X= 0.2034394 or 14.50799581 . I hope this helps

8 0

3 years ago

Consider this system of equations. Which equation represents the first equation written in slope-intercept form?

vlada-n [284]

Answer:

y= 5/2x - 5

Step-by-step explanation:

5x - 2y = 10

-5x -5x (Subtract both sides by 5x to leave y by itself)

-2y = -5x + 10

-2y/-2 = -5/-2 + 10/-2

(Divide both sides by -2 to leave y with no coefficient. -5/-2 = 5/2 because there are two negatives. 10/-2 = -5.

y = 5/2 - 5

4 0

3 years ago

Read 2 more answers

A. -4m - 12 - 5m = 13

vladimir2022 [97]

Answer:

Hope this helps!

Step-by-step explanation:

6 0

3 years ago

Determine whether f(x)=5x+1/x and g(x)= x/5x+1 are inverse functions. Explain how you know.

vladimir1956 [14]

A property of inverse functions is that if f(x) = a, g(a) = x

F(x) = (5x+1)/x
G(x) = x/(5x+1)

Plug in x = 3.
F(3) = 16/3
G(16/3) = 16/83. Since it doesn’t equal 3, it’s not an inverse function

4 0

3 years ago

Read 2 more answers